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George Em Karniadakis

George Em Karniadakis

Brown University
United States

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Mathematics
USA
2026
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Mechanical and Aerospace Engineering
USA
2026

D-Index & Metrics

Discipline name D-Index World Ranking Current World Ranking National Ranking Current National Ranking Publications Citations
Mathematics 139 1 1 1 1 760 103227
Mechanical and Aerospace Engineering 133 9 8 5 4 820 99712
Physics 135 462 445 258 247 743 99796

George Em Karniadakis publications per year

The chart shows the history of publications by George Em Karniadakis between 1986 and 2026, highlighting the no. of papers published in each year and offering an overview of the publication velocity of this scholar. George Em Karniadakis published across 41 years, from 1986 to 2026, averaging 29.7 papers a year. Output peaked at 92 publications in 2024. 56 of the 1,217 publications appeared in the last two years.

No. of publications
20 40 60 80
Bar chart. Horizontal axis: year, 1986 to 2026. Vertical axis: number of publications, 0 to 92. Peak 92 publications in 2024. 1986: 4 publications 1987: 0 publications 1988: 3 publications 1989: 4 publications 1990: 6 publications 1991: 13 publications 1992: 6 publications 1993: 15 publications 1994: 5 publications 1995: 10 publications 1996: 11 publications 1997: 8 publications 1998: 9 publications 1999: 19 publications 2000: 15 publications 2001: 13 publications 2002: 26 publications 2003: 36 publications 2004: 27 publications 2005: 39 publications 2006: 32 publications 2007: 20 publications 2008: 24 publications 2009: 33 publications 2010: 29 publications 2011: 34 publications 2012: 26 publications 2013: 38 publications 2014: 37 publications 2015: 59 publications 2016: 42 publications 2017: 58 publications 2018: 42 publications 2019: 44 publications 2020: 57 publications 2021: 82 publications 2022: 59 publications 2023: 84 publications 2024: 92 publications 2025: 54 publications 2026: 2 publications
1986 2026

1,217 publications in total across all disciplines

View publications per year as a table
George Em Karniadakis: publications per year, 1986 to 2026
Year Publications
1986 4
1987 0
1988 3
1989 4
1990 6
1991 13
1992 6
1993 15
1994 5
1995 10
1996 11
1997 8
1998 9
1999 19
2000 15
2001 13
2002 26
2003 36
2004 27
2005 39
2006 32
2007 20
2008 24
2009 33
2010 29
2011 34
2012 26
2013 38
2014 37
2015 59
2016 42
2017 58
2018 42
2019 44
2020 57
2021 82
2022 59
2023 84
2024 92
2025 54
2026 2
Total 1,217
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George Em Karniadakis publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where George Em Karniadakis sits on this spectrum.

No. of scientists
25 50 75 100
Bar chart with 100 bars. Horizontal axis: publications, 42–46 to 537+. Vertical axis: number of scientists, 0 to 112. Most scientists, 112, have 142–146 publications. The last bar groups every scientist with 537 publications or more. The highlighted bar, 537+ publications, is where this scientist sits. 42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientist 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientist 522–526 publications: 3 scientists 527–531 publications: 1 scientist 532–536 publications: 4 scientists 537+ publications: 100 scientists
42–46 publications 537+

This scientist: 760 publications — 99th percentile

99% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

View publications distribution as a table
Number of Mathematics scientists by publication count, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
Publications Scientists This scientist
42–46 3
47–51 5
52–56 7
57–61 20
62–66 14
67–71 25
72–76 19
77–81 35
82–86 50
87–91 60
92–96 86
97–101 84
102–106 83
107–111 90
112–116 99
117–121 90
122–126 91
127–131 109
132–136 110
137–141 98
142–146 112
147–151 102
152–156 88
157–161 106
162–166 83
167–171 102
172–176 77
177–181 81
182–186 78
187–191 71
192–196 92
197–201 64
202–206 69
207–211 64
212–216 62
217–221 58
222–226 53
227–231 50
232–236 46
237–241 46
242–246 46
247–251 43
252–256 29
257–261 45
262–266 30
267–271 33
272–276 34
277–281 30
282–286 31
287–291 21
292–296 34
297–301 26
302–306 10
307–311 17
312–316 23
317–321 13
322–326 16
327–331 26
332–336 13
337–341 13
342–346 16
347–351 17
352–356 12
357–361 18
362–366 18
367–371 9
372–376 11
377–381 8
382–386 8
387–391 9
392–396 9
397–401 8
402–406 11
407–411 6
412–416 6
417–421 9
422–426 8
427–431 5
432–436 8
437–441 8
442–446 4
447–451 4
452–456 4
457–461 2
462–466 2
467–471 4
472–476 3
477–481 3
482–486 6
487–491 3
492–496 5
497–501 5
502–506 1
507–511 6
512–516 4
517–521 1
522–526 3
527–531 1
532–536 4
537+ 100 760
Download as CSV

George Em Karniadakis D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where George Em Karniadakis sits on this spectrum.

No. of scientists
50 100 150
Bar chart with 57 bars. Horizontal axis: D-Index, 30 to 86+. Vertical axis: number of scientists, 0 to 174. Most scientists, 174, have 30 D-Index. The last bar groups every scientist with 86 D-Index or more. The highlighted bar, 86+ D-Index, is where this scientist sits. 30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 139 D-Index — 100th percentile

100% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

View D-Index distribution as a table
Number of Mathematics scientists by D-index, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
D-Index Scientists This scientist
30 174
31 151
32 174
33 117
34 136
35 127
36 145
37 153
38 150
39 150
40 138
41 136
42 93
43 108
44 115
45 112
46 103
47 75
48 59
49 67
50 60
51 57
52 59
53 62
54 60
55 50
56 42
57 54
58 50
59 42
60 41
61 35
62 40
63 21
64 31
65 27
66 29
67 19
68 25
69 17
70 18
71 12
72 14
73 13
74 18
75 9
76 11
77 10
78 9
79 16
80 12
81 10
82 5
83 5
84 13
85 6
86+ 99 139
Download as CSV

Research.com Recognitions

  • 2026 - Research.com Mathematics in United States Leader Award
  • 2026 - Research.com Mechanical and Aerospace Engineering in United States Leader Award
  • 2025 - Research.com Mathematics in United States Leader Award
  • 2025 - Research.com Mechanical and Aerospace Engineering in United States Leader Award
  • 2018 - Fellow of the American Association for the Advancement of Science (AAAS)
  • 2013 - THE J. TINSLEY ODEN MEDAL For outstanding contributions to stochastic differential equations, in particular modelling uncertainty with polynomial chaos and development of spectral and hp element methods on unstructured meshes
  • 2011 - ACM Gordon Bell Prize For "A new computational paradigm in multiscale simulations: Application to brain-blood flow."
  • 2010 - SIAM Fellow For contributions to stochastic modeling, spectral elements, and fluid mechanics.
  • 2007 - THE THOMAS J.R. HUGHES MEDAL
  • 2004 - Fellow of American Physical Society (APS) Citation For his innovative developments and his insightful applications of the spectralelement method in computational fluid dynamics
  • 2002 - Fellow of the American Society of Mechanical Engineers

Overview

George Em Karniadakis is affiliated with Brown University in the United States. Their research work spans multiple fields of study, with a significant focus on engineering and physics and astronomy.

Their main subfields of study include statistical and nonlinear physics, artificial intelligence, computational mechanics, aerospace engineering, and materials chemistry. Their research topics cover model reduction and neural networks, neural networks and applications, fluid dynamics and turbulent flows, probabilistic and robust engineering design, nuclear engineering thermal-hydraulics, blood properties and coagulation, and Gaussian processes and Bayesian inference.

George Em Karniadakis has contributed to several research publications and academic venues. Frequent publication venues include:

  • arXiv (Cornell University)
  • Journal of Computational Physics
  • Computer Methods in Applied Mechanics and Engineering
  • SSRN Electronic Journal
  • SIAM Journal on Scientific Computing

Recent notable papers authored or co-authored by George Em Karniadakis are:

  • Physics-informed machine learning, 2021, Nature Reviews Physics
  • Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, 2020, Science
  • Physics-informed neural networks (PINNs) for fluid mechanics: a review, 2021, Acta Mechanica Sinica
  • NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations, 2020, Journal of Computational Physics
  • Physics-Informed Neural Networks for Heat Transfer Problems, 2021, Journal of Heat Transfer

The scientist has co-authored extensively with collaborators including Khemraj Shukla, Somdatta Goswami, Zongren Zou, Xuhui Meng, and Ameya D. Jagtap.

In addition to journal publications, George Em Karniadakis has contributed to academic books, notably one published by Cambridge University Press titled Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations in 2024.

Awards received by George Em Karniadakis include:

  • Fellow of the American Association for the Advancement of Science (AAAS), 2018
  • THE J. TINSLEY ODEN MEDAL, 2013, for contributions to stochastic differential equations and development of spectral and hp element methods on unstructured meshes
  • ACM Gordon Bell Prize, 2011, for work on multiscale brain-blood flow simulations
  • SIAM Fellow, 2010, for contributions to stochastic modeling, spectral elements, and fluid mechanics
  • THE THOMAS J.R. HUGHES MEDAL, 2007
  • Fellow of American Physical Society (APS), 2004, for developments in computational fluid dynamics via spectral-element methods
  • Fellow of the American Society of Mechanical Engineers, 2002

Best Publications

  • Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

    Maziar Raissi;Paris Perdikaris;George E. Karniadakis

  • The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

    Dongbin Xiu;George Em Karniadakis

  • Physics-informed machine learning

    George Em Karniadakis;Ioannis G. Kevrekidis;Lu Lu;Paris Perdikaris

  • Spectral/hp Element Methods for Computational Fluid Dynamics

    George Karniadakis;Spencer J. Sherwin

  • Microflows and Nanoflows: Fundamentals and Simulation

    George E Karniadakis

  • DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

    Lu Lu;Pengzhan Jin;George Em Karniadakis

  • The Development of Discontinuous Galerkin Methods

    Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu

  • Physics-informed neural networks (PINNs) for fluid mechanics: a review

    Unknown

  • High-order splitting methods for the incompressible Navier-Stokes equations

    George Em Karniadakis;Moshe Israeli;Steven A Orszag

  • Modeling uncertainty in flow simulations via generalized polynomial chaos

    Dongbin Xiu;George Em Karniadakis

  • Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations.

    Maziar Raissi;Maziar Raissi;Alireza Yazdani;George Em Karniadakis

  • DeepXDE: A deep learning library for solving differential equations

    Lu Lu;Xuhui Meng;Zhiping Mao;George Em Karniadakis

  • REPORT: A MODEL FOR FLOWS IN CHANNELS, PIPES, AND DUCTS AT MICRO AND NANO SCALES

    Ali Beskok;George Em Karniadakis

  • Spectral/hp Element Methods for CFD

    George Em Karniadakis;Spencer J Sherwin

  • Hidden physics models: Machine learning of nonlinear partial differential equations

    Maziar Raissi;George Em Karniadakis

  • Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

    Maziar Raissi;Paris Perdikaris;George Em Karniadakis

  • Physics-informed neural networks for high-speed flows

    Zhiping Mao;Ameya D. Jagtap;George Em Karniadakis

  • NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

    Xiaowei Jin;Shengze Cai;Hui Li;George Em Karniadakis

  • Discontinuous Galerkin Methods: Theory, Computation and Applications

    Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu

  • Physics-informed neural networks for inverse problems in nano-optics and metamaterials.

    Yuyao Chen;Lu Lu;George Em Karniadakis;Luca Dal Negro

  • Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

    Dongbin Xiu;George Em Karniadakis

  • An adaptive multi-element generalized polynomial chaos method for stochastic differential equations

    Xiaoliang Wan;George Em Karniadakis

  • Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

    Lu Lu;Pengzhan Jin;Pengzhan Jin;Guofei Pang;Zhongqiang Zhang

Frequent Co-Authors

Paris Perdikaris
Paris Perdikaris University of Pennsylvania
Michael S. Triantafyllou
Michael S. Triantafyllou MIT
Ming Dao
Ming Dao MIT
Spencer J. Sherwin
Spencer J. Sherwin Imperial College London
Suchuan Dong
Suchuan Dong Purdue University West Lafayette
Martin R. Maxey
Martin R. Maxey Brown University
Robert M. Kirby
Robert M. Kirby University of Utah
Subra Suresh
Subra Suresh MIT
Dongbin Xiu
Dongbin Xiu The Ohio State University
Guang Lin
Guang Lin Purdue University West Lafayette

External Links

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Best Scientists Citing George Em Karniadakis

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Spencer J. Sherwin

Imperial College London

Publications: 162

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Mark Christopher Thompson

Monash University

Publications: 92

Robert M. Kirby

Robert M. Kirby

University of Utah

Publications: 75

Kerry Hourigan

Kerry Hourigan

Monash University

Publications: 70

Bruno Sudret

Bruno Sudret

ETH Zurich

Publications: 69

Dongbin Xiu

Dongbin Xiu

The Ohio State University

Publications: 62

Guang Lin

Guang Lin

Purdue University West Lafayette

Publications: 58

Gianluca Iaccarino

Gianluca Iaccarino

Stanford University

Publications: 58

Bernd R. Noack

Bernd R. Noack

Harbin Institute of Technology

Publications: 53

Alfio Quarteroni

Alfio Quarteroni

Polytechnic University of Milan

Publications: 52

Roger Ghanem

Roger Ghanem

University of Southern California

Publications: 48

Gerhard Gompper

Gerhard Gompper

Forschungszentrum Jülich

Publications: 48

Hugh Maurice Blackburn

Hugh Maurice Blackburn

Monash University

Publications: 45

Omar M. Knio

Omar M. Knio

King Abdullah University of Science and Technology

Publications: 44

Dongxiao Zhang

Dongxiao Zhang

Southern University of Science and Technology

Publications: 42

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Ioannis G. Kevrekidis

Johns Hopkins University

Publications: 42

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